Data-driven multi-objective optimization of explosively formed projectiles using central composite design

The terminal ballistic performance of Explosively Formed Projectiles (EFP) is governed by highly non-linear interactions between liner geometry and explosive characteristics. To address this complexity, a rigorous multi-objective optimization framework is established by integrating the Box-Wilson Central Composite Design (CCD) with explicit dynamics simulations. The interactive effects of liner height (h/d), top thickness (δ₁/d), edge thickness (δ₂/d), and charge length (l/d) are systematically quantified. Numerical models, validated against static firing experiments, demonstrate high predictive reliability with relative errors consistently below 6%. Statistical analysis reveals that top thickness dictates kinematic performance, contributing over 98% to velocity variance, while an energy saturation plateau is identified at a charge length ratio of l/d ≈ 1.2. Through constrained desirability optimization, an optimal configuration (h/d=0.221, δ₁/d=0.032, δ₂/d=0.012, l/d=1.215) is derived, achieving a terminal velocity of 2405 m/s, a penetration depth of 29.0 mm, and a hole diameter of 31.0 mm. Confirmatory simulations capture a significant dynamic necking effect at high velocities, effectively concentrating mass along the penetration axis and reducing target resistance. Consequently, the optimized projectile penetrates 24.4% deeper than statistical predictions and outperforms baseline designs by 34.9% in velocity, demonstrating the framework's efficacy for advanced warhead engineering.